
For suitable choice of \(\delta \in (0,1)\) , from [1]} (see the expression for \(g(t)\)  there), we have
\(\left[ 1+c\delta \frac{\bar{u}(x)-\bar{u}(y)}{\bar{u}(x)} -\frac{\bar{u}(x)^{m-1}}{\bar{u}(y)^{m-1}} \right] \le 0,\) 
